Yes, there can be a pure imaginary imaginary solution, as i2 =-1 and -i2 = 1. Or there can be a pure real solution or there can be a complex solution.
For a quadratic equation ax2+ bx + c = 0, it depends on the value of the discriminant [b2 - 4ac], which is the value inside the radical of the quadratic formula.
Write the quadratic equation in the standard form: ax2 + bx + c = 0 Then calculate the discriminant = b2 - 4ac If the discriminant is greater than zero, there are two distinct real solutions. If the discriminant is zero, there is one real solution. If the discriminany is less than zero, there are no real solutions (there will be two distinct imaginary solutions).
The term "discriminant" is usually used for quadratic equations. If the discriminant is zero, then the equation has exactly one solution.
No. Sometimes they are both extraneous.
If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.
C
The answer depends on the nature of the equation. Just as there are different ways of solving a linear equation with a real solution and a quadratic equation with real solutions, and other kinds of equations, there are different methods for solving different kinds of imaginary equations.
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
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Is it possible for a quadratic equation to have no real solution? please give an example and explain. Thank you
It has one real solution.
No. A quadratic may have two identical real solutions, two different real solutions, ortwo conjugate complex solutions (including pure imaginary).It can't have one real and one complex or imaginary solution.
When there is a negative number under the square root in a quadratic equation, it indicates that the equation has no real solutions. Instead, it results in complex or imaginary solutions, as the square root of a negative number involves the imaginary unit (i). This situation occurs when the discriminant (the part under the square root in the quadratic formula) is negative. Consequently, the quadratic graph does not intersect the x-axis, indicating no real roots.
A quadratic equation can have two solutions, one solution, or no real solutions, depending on its discriminant (the part of the quadratic formula under the square root). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is exactly one real solution (a repeated root); and if it is negative, there are no real solutions, only complex ones. Thus, a quadratic equation does not always have two solutions.
If the discriminant of a quadratic equation is less than zero, it indicates that the equation has no real solutions. Instead, it has two complex (or imaginary) solutions that are conjugates of each other. This means the parabola represented by the quadratic equation does not intersect the x-axis.